Question: Let $f(x)=x+3$ and $g(x)=3x+5$.  Find $f(g(4))-g(f(4))$.
Solution: We have $g(4) = 3\cdot 4 + 5= 17$, so $f(g(4)) = f(17) = 17 + 3 = 20$. We also have $f(4) = 4+3 = 7$, so $g(f(4)) = g(7)=3\cdot 7 + 5 = 26$.  Therefore, $f(g(4)) - g(f(4)) = 20 - 26 = \boxed{-6}$.